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Proof step 11 from proof putByteArray-vals-addarray (previous step)

0 ≤ j ⊦ (putArray(mkjavavalues(bytes), r, j, addarray(r, initial_value(byte_type), n→i(# bytes) + j, st))[r -- _type, typeval(mkarraytype(byte_type))] [r -- _length, intval(n→i(# bytes) + j) ] ) = (addarray(r, mklist(initial_value(byte_type), i→n(j)) + mkjavavalues(bytes), 0, st)[r -- _type, typeval(mkarraytype(byte_type))] [r -- _length, intval(j + n→i(# bytes)) ] )

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ 0 ≤ j ∧ j ≤ i ∧ i ≤ j + n→i(# vals) → putArray(vals, r, j, addarray(r, val, i, st)) = addarray(r, mklist(val, i→n(j)) + vals, 0, st)

Rule argument

[crewrite-arg: putarray-addarray , F , [st, i, val, j, r, vals] → [st, n→i(# bytes) + j, initial_value(byte_type), j, r, mkjavavalues(bytes)] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j < j ↔ i < 0], [CSIMPSEQ : ⊦ ¬ n→i(n) < 0], [CSIMPSEQ : ⊦ # mkjavavalues(bytes) = # bytes], [CSIMPSEQ : ⊦ i + j ≤ i0 + j ↔ i ≤ i0], [CSIMPSEQ : ⊦ n→i(m) ≤ n→i(n) ↔ m ≤ n], [CSIMPSEQ : ⊦ ¬ m ≤ n ↔ n < m], [CSIMPSEQ : ⊦ ¬ n < n])], [EXTRATERMS : (st, n→i(# bytes) + j, initial_value(byte_type), j, r, mkjavavalues(bytes))]]